中文摘要：

该文扩展了U变换-有限元法分析弹性矩形薄板的范围。通过构造一个与简支、固支或二种边界条件组合的矩形板的等效系统，使刚度矩阵成为循环矩阵，采用U变换，成功解耦了有限元矩阵方程，使得有限元计算只须在一个单元上进行。给出了承受板中集中载荷和对边均布弯矩两种载荷形式下的板中挠度解析表达式。所得到的级数解不仅计算效率高，还能给出误差估计的显式表达式，能够直接掌控计算精度。算例中考察了几种不同边界条件下的计算结果，与已有理论结果的对比说明，该方法提高了计算的精度和效率。

英文摘要：

The U-Transformation-Finite Element method for a rectangular thin plate is extended in this paper. The stiffness matrix is converted to a cyclic matrix by establishing an equivalent system for the rectangular thin plate with simply-supported boundary conditions or clamped boundary conditions, and their combination. Then the finite element matrix equation is uncoupled by adopting U-transformation, resulting in the calculation which can be performed in one element. The series of solution to deflections of the central point for the square plate, subjected to a concentrated force acted at the center of the plate and to a uniform bending moment acted on the two opposite edges, is given out. It could give an explicit expression of the error estimation and control the computational accuracy. Calculation examples for several different boundary conditions show that the present result has high efficiency and precision compared with existing results.